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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* $Id: matching.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
(*i*)
open Util
open Names
open Libnames
open Nameops
open Termops
open Reductionops
open Term
open Rawterm
open Sign
open Environ
open Pattern
(*i*)
(* Given a term with second-order variables in it,
represented by Meta's, and possibly applied using [SOAPP] to
terms, this function will perform second-order, binding-preserving,
matching, in the case where the pattern is a pattern in the sense
of Dale Miller.
ALGORITHM:
Given a pattern, we decompose it, flattening Cast's and apply's,
recursing on all operators, and pushing the name of the binder each
time we descend a binder.
When we reach a first-order variable, we ask that the corresponding
term's free-rels all be higher than the depth of the current stack.
When we reach a second-order application, we ask that the
intersection of the free-rels of the term and the current stack be
contained in the arguments of the application, and in that case, we
construct a LAMBDA with the names on the stack.
*)
exception PatternMatchingFailure
let constrain (n,m) sigma =
if List.mem_assoc n sigma then
if eq_constr m (List.assoc n sigma) then sigma
else raise PatternMatchingFailure
else
(n,m)::sigma
let build_lambda toabstract stk (m : constr) =
let rec buildrec m p_0 p_1 = match p_0,p_1 with
| (_, []) -> m
| (n, (na,t)::tl) ->
if List.mem n toabstract then
buildrec (mkLambda (na,t,m)) (n+1) tl
else
buildrec (lift (-1) m) (n+1) tl
in
buildrec m 1 stk
let memb_metavars m n =
match (m,n) with
| (None, _) -> true
| (Some mvs, n) -> List.mem n mvs
let eq_context ctxt1 ctxt2 = array_for_all2 eq_constr ctxt1 ctxt2
let same_case_structure (_,cs1,ind,_) ci2 br1 br2 =
match ind with
| Some ind -> ind = ci2.ci_ind
| None -> cs1 = ci2.ci_cstr_nargs
let matches_core convert allow_partial_app pat c =
let rec sorec stk sigma p t =
let cT = strip_outer_cast t in
match p,kind_of_term cT with
| PSoApp (n,args),m ->
let relargs =
List.map
(function
| PRel n -> n
| _ -> error "Only bound indices allowed in second order pattern matching.")
args in
let frels = Intset.elements (free_rels cT) in
if list_subset frels relargs then
constrain (n,build_lambda relargs stk cT) sigma
else
raise PatternMatchingFailure
| PMeta (Some n), m ->
let depth = List.length stk in
if depth = 0 then
(* Optimisation *)
constrain (n,cT) sigma
else
let frels = Intset.elements (free_rels cT) in
if List.for_all (fun i -> i > depth) frels then
constrain (n,lift (-depth) cT) sigma
else
raise PatternMatchingFailure
| PMeta None, m -> sigma
| PRef (VarRef v1), Var v2 when v1 = v2 -> sigma
| PVar v1, Var v2 when v1 = v2 -> sigma
| PRef ref, _ when constr_of_global ref = cT -> sigma
| PRel n1, Rel n2 when n1 = n2 -> sigma
| PSort (RProp c1), Sort (Prop c2) when c1 = c2 -> sigma
| PSort (RType _), Sort (Type _) -> sigma
| PApp (p, [||]), _ -> sorec stk sigma p t
| PApp (PApp (h, a1), a2), _ ->
sorec stk sigma (PApp(h,Array.append a1 a2)) t
| PApp (PMeta (Some n),args1), App (c2,args2) when allow_partial_app ->
let p = Array.length args2 - Array.length args1 in
if p>=0 then
let args21, args22 = array_chop p args2 in
let sigma =
let depth = List.length stk in
let c = mkApp(c2,args21) in
let frels = Intset.elements (free_rels c) in
if List.for_all (fun i -> i > depth) frels then
constrain (n,lift (-depth) c) sigma
else
raise PatternMatchingFailure in
array_fold_left2 (sorec stk) sigma args1 args22
else raise PatternMatchingFailure
| PApp (c1,arg1), App (c2,arg2) ->
(try array_fold_left2 (sorec stk) (sorec stk sigma c1 c2) arg1 arg2
with Invalid_argument _ -> raise PatternMatchingFailure)
| PProd (na1,c1,d1), Prod(na2,c2,d2) ->
sorec ((na2,c2)::stk) (sorec stk sigma c1 c2) d1 d2
| PLambda (na1,c1,d1), Lambda(na2,c2,d2) ->
sorec ((na2,c2)::stk) (sorec stk sigma c1 c2) d1 d2
| PLetIn (na1,c1,d1), LetIn(na2,c2,t2,d2) ->
sorec ((na2,t2)::stk) (sorec stk sigma c1 c2) d1 d2
| PRef (ConstRef _ as ref), _ when convert <> None ->
let (env,evars) = Option.get convert in
let c = constr_of_global ref in
if is_conv env evars c cT then sigma
else raise PatternMatchingFailure
| PIf (a1,b1,b1'), Case (ci,_,a2,[|b2;b2'|]) ->
let ctx,b2 = decompose_lam_n_assum ci.ci_cstr_nargs.(0) b2 in
let ctx',b2' = decompose_lam_n_assum ci.ci_cstr_nargs.(1) b2' in
let n = rel_context_length ctx in
let n' = rel_context_length ctx' in
if noccur_between 1 n b2 & noccur_between 1 n' b2' then
let s = List.fold_left (fun l (na,_,t) -> (na,t)::l) stk ctx in
let s' = List.fold_left (fun l (na,_,t) -> (na,t)::l) stk ctx' in
let b1 = lift_pattern n b1 and b1' = lift_pattern n' b1' in
sorec s' (sorec s (sorec stk sigma a1 a2) b1 b2) b1' b2'
else
raise PatternMatchingFailure
| PCase (ci1,p1,a1,br1), Case (ci2,p2,a2,br2) ->
if same_case_structure ci1 ci2 br1 br2 then
array_fold_left2 (sorec stk)
(sorec stk (sorec stk sigma a1 a2) p1 p2) br1 br2
else
raise PatternMatchingFailure
| PFix c1, Fix _ when eq_constr (mkFix c1) cT -> sigma
| PCoFix c1, CoFix _ when eq_constr (mkCoFix c1) cT -> sigma
| _ -> raise PatternMatchingFailure
in
Sort.list (fun (a,_) (b,_) -> a<b) (sorec [] [] pat c)
let matches = matches_core None true
let pmatches = matches_core None true
(* To skip to the next occurrence *)
exception NextOccurrence of int
(* Tells if it is an authorized occurrence and if the instance is closed *)
let authorized_occ nocc mres =
if not (List.for_all (fun (_,c) -> closed0 c) (fst mres)) then
raise PatternMatchingFailure;
if nocc = 0 then mres
else raise (NextOccurrence nocc)
let special_meta = (-1)
(* Tries to match a subterm of [c] with [pat] *)
let rec sub_match nocc pat c =
match kind_of_term c with
| Cast (c1,k,c2) ->
(try authorized_occ nocc ((matches pat c), mkMeta special_meta) with
| PatternMatchingFailure ->
let (lm,lc) = try_sub_match nocc pat [c1] in
(lm,mkCast (List.hd lc, k,c2))
| NextOccurrence nocc ->
let (lm,lc) = try_sub_match (nocc - 1) pat [c1] in
(lm,mkCast (List.hd lc, k,c2)))
| Lambda (x,c1,c2) ->
(try authorized_occ nocc ((matches pat c), mkMeta special_meta) with
| PatternMatchingFailure ->
let (lm,lc) = try_sub_match nocc pat [c1;c2] in
(lm,mkLambda (x,List.hd lc,List.nth lc 1))
| NextOccurrence nocc ->
let (lm,lc) = try_sub_match (nocc - 1) pat [c1;c2] in
(lm,mkLambda (x,List.hd lc,List.nth lc 1)))
| Prod (x,c1,c2) ->
(try authorized_occ nocc ((matches pat c), mkMeta special_meta) with
| PatternMatchingFailure ->
let (lm,lc) = try_sub_match nocc pat [c1;c2] in
(lm,mkProd (x,List.hd lc,List.nth lc 1))
| NextOccurrence nocc ->
let (lm,lc) = try_sub_match (nocc - 1) pat [c1;c2] in
(lm,mkProd (x,List.hd lc,List.nth lc 1)))
| LetIn (x,c1,t2,c2) ->
(try authorized_occ nocc ((matches pat c), mkMeta special_meta) with
| PatternMatchingFailure ->
let (lm,lc) = try_sub_match nocc pat [c1;t2;c2] in
(lm,mkLetIn (x,List.hd lc,List.nth lc 1,List.nth lc 2))
| NextOccurrence nocc ->
let (lm,lc) = try_sub_match (nocc - 1) pat [c1;t2;c2] in
(lm,mkLetIn (x,List.hd lc,List.nth lc 1,List.nth lc 2)))
| App (c1,lc) ->
(try authorized_occ nocc ((matches pat c), mkMeta special_meta) with
| PatternMatchingFailure ->
let (lm,le) = try_sub_match nocc pat (c1::(Array.to_list lc)) in
(lm,mkApp (List.hd le, Array.of_list (List.tl le)))
| NextOccurrence nocc ->
let (lm,le) = try_sub_match (nocc - 1) pat (c1::(Array.to_list lc)) in
(lm,mkApp (List.hd le, Array.of_list (List.tl le))))
| Case (ci,hd,c1,lc) ->
(try authorized_occ nocc ((matches pat c), mkMeta special_meta) with
| PatternMatchingFailure ->
let (lm,le) = try_sub_match nocc pat (c1::Array.to_list lc) in
(lm,mkCase (ci,hd,List.hd le,Array.of_list (List.tl le)))
| NextOccurrence nocc ->
let (lm,le) = try_sub_match (nocc - 1) pat (c1::Array.to_list lc) in
(lm,mkCase (ci,hd,List.hd le,Array.of_list (List.tl le))))
| Construct _ | Fix _ | Ind _|CoFix _ |Evar _|Const _
| Rel _|Meta _|Var _|Sort _ ->
(try authorized_occ nocc ((matches pat c),mkMeta special_meta) with
| PatternMatchingFailure -> raise (NextOccurrence nocc)
| NextOccurrence nocc -> raise (NextOccurrence (nocc - 1)))
(* Tries [sub_match] for all terms in the list *)
and try_sub_match nocc pat lc =
let rec try_sub_match_rec nocc pat lacc = function
| [] -> raise (NextOccurrence nocc)
| c::tl ->
(try
let (lm,ce) = sub_match nocc pat c in
(lm,lacc@(ce::tl))
with
| NextOccurrence nocc -> try_sub_match_rec nocc pat (lacc@[c]) tl) in
try_sub_match_rec nocc pat [] lc
let match_subterm nocc pat c =
try sub_match nocc pat c
with NextOccurrence _ -> raise PatternMatchingFailure
let is_matching pat n =
try let _ = matches pat n in true
with PatternMatchingFailure -> false
let matches_conv env sigma = matches_core (Some (env,sigma)) false
let is_matching_conv env sigma pat n =
try let _ = matches_conv env sigma pat n in true
with PatternMatchingFailure -> false
|